Tutorial Area of a Sector


Area of a Sector


   


A sector is a portion of a circle bounded by two radii and the arc joining their extremities. It is thus a form of triangle with a covered base. In the figure the portion is a sector. Arc is called the arc of the sector and is called the angle of the sector.


The area of a sector of a circle is equal to a fraction of the area of the circle determined by dividing the size of the angle by. Thus, if the angle of the sector is , the area of the sector is or the area of the circle, that is, i.e., the area of a sector bears that portion to the area of the circle which its angle bears to right angles i.e., .

(a) If the angle is given in degrees, say, then
Area of the sector,
Length of the arc,
(b) If the angle is given in radians, say radians, then
Area of the sector,
(c) If the length of the arc and the radius of the circle are given, then
Area of the sector, where

Example:
Find the area of a sector of in a circle of radius cm.
Solution:
The sector has angle.


Its area is equal to
Since radius cm
Therefore Square

Example:
The minute hand of a clock is cw long. Find the area which is described on the clock face between A.M to A.M.
Solution:
Given that, Length of minute hand, radius cm
Minutes
Minutes
Since, Area of sector

Square cm


Exclusive Topics

Higher Mathematics

Other Math Links

  • Math for Programmers
  • Newsletter